Engineering is one of things that people will always need. The unemployment statistics you are talking about are probably more related to production jobs (in the engineering world). So there may be strain on the market, but a good engineer can work almost anywhere, independant of their field. I know of mechanical engineers working in banks, of aeronautical engineers working in commercial product design (me ) and in the petro chemical industry and chemical engineers working for car companies.

Engineering is a good choice and I think that you should focus rather on a field that you will enjoy than on one that promises the best jobs etc. A lot of my friends in highschool started going into IT because there was so much demand for it in the late nineties, but they became a little unstuck when the market saturated and there were just too many ITers. Then you have a bunch of guys that studied something they didn't really want to, because they wanted the promised job security and then ended up having to study further in other fields to get a job and were ultimately unhappy.

Chemical and petroleum engineering is big at the moment, I'm not sure for how much longer. Bio-engineering I think has a good steady market. Electrical engineering is probably a safe bet with a lot more things going digital these days and electric cars and other vehicles coming more and more to the forefront. Computer engineering... not sure. Mech Eng and material science is pretty stable too and the job opportunities are diverse.

Engineering as a whole is a safe bet...the primary driver in pretty much all industries in modern times is dependent on the development of technologies and I'm sure you hear it a lot but we're always going to have a need for engineers.

Especially even more so around now, given the lack of graduating engineers in the U.S.

The answer depends a lot more on the industry than on what your major is. Some
industries (like the current auto industry) will be transformed in 20 years as the
products evolve. Others like the composites industry will grow but not change
dramatically as the need grows.

If you are concerned about employment you should focus on a more general program
like mechanical or electrical and let specialization come later if you want to pursue
graduate school.

You can't go wrong with a classic engineering education. As someone said above
you can work in almost any industry doing almost anything.